Problem: Simplify the following expression: $10\sqrt{175}$.
First, try to factor a perfect square out of the radical. $= 10\sqrt{175}$ $= 10\sqrt{25 \cdot 7}$ Separate the radical and simplify. $= 10\sqrt{25} \cdot \sqrt{7}$ $= 10 \cdot 5 \cdot \sqrt{7}$ $= 50\sqrt{7}$